Unitary Matrix Models and Painlevé III

Details Unitary Matrix Models and Painlevé III Unitary Matrix Models and Painlevé III

1996-09-27

arxiv.org/abs/hep-th/9609214v2

Mod.Phys.Lett. A11 (1996) 3001-3010

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX, final version to appear in Mod. Phys. Lett. A

Scientific paper

10.1142/S0217732396002976

We discussed the full unitary matrix models from the view points of integrable equations and string equations. Coupling the Toda equations and the string equations, we derive a special case of the Painlev\'{e} III equation. From the Virasoro constrains, we can use the radial coordinate. The relation between $t_{1}$ and $t_{-1}$ is like the complex conjugate. %An implicit to the $t\bar{t}$ fusion of topological sigma model %is therby expected.

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